Normal mode calculations of icosahedral viruses with full dihedral flexibility by use of molecular symmetry

Biomechanical Sensing Using Gas Bubbles Oscillations in Liquids and Adjacent Technologies: Theory and Practical Applications

Gas bubbles present in liquids underpin many natural phenomena and human-developed technologies that improve the quality of life. Since all living organisms are predominantly made of water, they may also contain bubbles-introduced both naturally and artificially-that can serve as biomechanical sensors operating in hard-to-reach places inside a living body and emitting signals that can be detected by common equipment used in ultrasound and photoacoustic imaging procedures. This kind of biosensor is the focus of the present article, where we critically review the emergent sensing technologies based on acoustically driven oscillations of bubbles in liquids and bodily fluids. This review is intended for a broad biosensing community and transdisciplinary researchers translating novel ideas from theory to experiment and then to practice. To this end, all discussions in this review are written in a language that is accessible to non-experts in specific fields of acoustics, fluid dynamics and acousto-optics.

The functional motions and related key residues behind the uncoating of coxsackievirus A16

The coxsackievirus A16 (CVA16) is a highly contagious virus that causes the hand, foot, and mouth disease, which seriously threatens the health of children. At present, there are still no available antiviral drugs or effective treatments against the infection of CVA16, and thus it is of great significance to develop anti-CVA16 vaccines. However, the intrinsic uncoating property of the capsid may destroy the neutralizing epitopes and influence its immunogenicity, which hinders the vaccine developments. In the present work, the functional-quantity-based elastic network model analysis method developed by our group was extended to combine with group theory to investigate the uncoating motions of the CVA16 capsid, and then the functionally key residues controlling the uncoating motions were identified by our functional-quantity-based perturbation method. Several motion modes encoded in the topological structure of the capsid were revealed to be responsible for the uncoating of CVA16 particle. These modes predominantly contribute to the fluctuation of the gyration radius of the capsid. Then, by using the perturbation method, four clusters of key sites involved in the uncoating motions were identified, whose perturbations induce significant changes in the fluctuation of the gyration radius. These key residues are mainly located at the 2-fold channels, the quasi 3-fold channels, the bottom of the canyons, and the inter-subunit interfaces around the 3-fold axes. Our studies are helpful for better understanding the uncoating mechanism of the CVA16 capsid and provide potential target sites to prevent the uncoating motions, which is valuable for the vaccine design against CVA16.

A minimal coarse-grained model for the low-frequency normal mode analysis of icosahedral viral capsids

The main goal of this work is the design of a coarse-grained theoretical model of minimal resolution for the study of the physical properties of icosahedral virus capsids within the linear-response regime. In this model the capsid is represented as an interacting many-body system whose composing elements are capsid subunits (capsomers), which are treated as three-dimensional rigid bodies. The total interaction potential energy is written as a sum of pairwise capsomer-capsomer interactions. Based on previous work [Gomez Llorente et al., Soft Matter, 2014, 10, 3560], a minimal and complete anisotropic binary interaction that includes a full Hessian matrix of independent force constants is proposed. In this interaction model, capsomers have rotational symmetry around an axis of order n > 2. The full coarse-grained model is applied to analyse the low-frequency normal-mode spectrum of icosahedral T = 1 capsids. The model performance is evaluated by fitting its predicted spectrum to the full-atom results for the Satellite Tobacco Necrosis Virus (STNV) capsid [Dykeman and Sankey, Phys. Rev. Lett., 2008, 100, 028101]. Two capsomer choices that are compatible with the capsid icosahedral symmetry are checked, namely pentamers (n = 5) and trimers (n = 3). Both subunit types provide fair fits, from which the magnitude of the coarse-grained force constants for a real virus is obtained. The model is able to uncover latent instabilities whose analysis is fully consistent with the current knowledge about the STNV capsid, which does not self-assemble in the absence of RNA and is thermally unstable. The straightforward generalisability of the model beyond the linear regime and its completeness make it a promising tool to theoretically interpret many experimental data such as those provided by the atomic force microscopy or even to better understand processes far from equilibrium such as the capsid self-assembly.

Normal Mode Analysis as a Routine Part of a Structural Investigation

Normal mode analysis (NMA) is a technique that can be used to describe the flexible states accessible to a protein about an equilibrium position. These states have been shown repeatedly to have functional significance. NMA is probably the least computationally expensive method for studying the dynamics of macromolecules, and advances in computer technology and algorithms for calculating normal modes over the last 20 years have made it nearly trivial for all but the largest systems. Despite this, it is still uncommon for NMA to be used as a component of the analysis of a structural study. In this review, we will describe NMA, outline its advantages and limitations, explain what can and cannot be learned from it, and address some criticisms and concerns that have been voiced about it. We will then review the most commonly used techniques for reducing the computational cost of this method and identify the web services making use of these methods. We will illustrate several of their possible uses with recent examples from the literature. We conclude by recommending that NMA become one of the standard tools employed in any structural study.

Identification of key sites controlling protein functional motions by using elastic network model combined with internal coordinates

The elastic network model (ENM) is an effective method to extract the intrinsic dynamical properties encoded in protein tertiary structures. We have proposed a new ENM-based analysis method to reveal the motion modes directly responsible for a specific protein function, in which an internal coordinate related to the specific function was introduced to construct the internal/Cartesian hybrid coordinate space. In the present work, the function-related internal coordinates combined with a linear perturbation method were applied to identify the key sites controlling specific protein functional motions. The change in the fluctuations of the internal coordinate in response to residue perturbation was calculated in the hybrid coordinate space by using the linear response theory. The residues with the large fluctuation changes were identified to be the key sites that allosterically control the specific protein function. Two proteins, i.e., human DNA polymerase β and the chaperonin from Methanococcus maripaludis, were investigated as case studies, in which several collective and local internal coordinates were applied to identify the functionally key residues of these two studied proteins. The calculation results are consistent with the experimental observations. It is found that different collective internal coordinates lead to similar results, where the predicted functionally key sites are located at similar positions in the protein structure. While for the local internal coordinates, the predicted key sites tend to be situated at the region near to the coordinate-involving residues. Our studies provide a starting point for further exploring other function-related internal coordinates for other interesting proteins.

Unraveling the Motions behind Enterovirus 71 Uncoating

Enterovirus 71 can be a severe pathogen in small children and immunocompromised adults. Virus uncoating is a critical step in the infection of the host cell; however, the mechanisms that control this process remain poorly understood. We applied normal mode analysis and perturbation response scanning to several complexes of the virus capsid and present a coarse-graining approach to analyze the full capsid. We show that our method offers an alternative to expressing the system as a set of rigid blocks and accounts for the interconnection between nodes within each subunit and protein interfaces across the capsid. In our coarse-grained approach, the modes associated with capsid expansion are captured in the first three nondegenerate modes and correspond to the changes observed in structural studies of the virus. We show that the resolution of the analysis may be modified without losing information on the global motions leading to uncoating. Perturbation response scanning revealed that a protomer cannot serve as a functional unit to explain deformations of the capsid. Instead, we define a pentamer as the minimum functional unit to investigate changes within the capsid. From the modal analysis and perturbation response scanning, we locate a hotspot region surrounding the fivefold axis. The range of the effect of these single, hotspot residues extend to 140 Å. The perturbation of internal capsid residues in this region displayed greatest propensity to capsid expansion, thus indicating the significant role that the RNA genome may play in triggering uncoating.

A complex multiscale virtual particle model based elastic network model (CMVP-ENM) for the normal mode analysis of biomolecular complexes

The CMVP-ENM for virus normal mode analysis. With a special ratio parameter, CMVP-ENM can characterize the multi-material properties of biomolecular complexes and systematically enhance or suppress the modes for different components.

A time and memory efficient recipe for fast normal mode computations of complexes with icosahedral symmetry

With the recent breakthroughs in experimental technologies, structure determination of extremely large assemblies, many with icosahedral symmetry, has been rapidly accelerating. Computational studies of their dynamics are important to deciphering their functions as well as to structural refinement but are challenged by their extremely large size, which ranges from hundreds of thousands to even millions of atoms. Group theory can be used to significantly speed up the normal mode computations of these symmetric complexes, but the derivation is often obscured by the complexity of group theory and consequently is not widely accessible. To address this problem, this work presents an easy recipe for normal mode computations of complexes with icosahedral symmetry. The recipe details how the Hessian matrix in symmetry coordinates can be constructed in a few easy steps of matrix multiplications, without going through the complexity of group theory. All the "ingredient" matrices required in the recipe are fully provided in the Supplemental Information for easy reproduction. The work is timely considering the expected large in-flux of many more icosahedral assemblies in the near future. The recipe uses a minimum amount of memory and solves the normal modes in a significantly reduced amount of time, making it feasible to perform normal mode computations of these assemblies on most computer systems.

Coarse-grained dynamics of supramolecules: Conformational changes in outer shells of Dengue viruses

While structural data on viruses are more and more common, information on their dynamics is much harder to obtain as those viruses form very large molecular complexes. In this paper, we propose a new method for computing the coarse-grained normal modes of such supra-molecules, NormalGo. A new formalism is developed to represent the Hessian of a quadratic potential using tensor products. This formalism is applied to the Tirion elastic potential, as well as to a Gō like potential. When combined with a fast method for computing a select set of eigenpairs of the Hessian, this new formalism enables the computation of thousands of normal modes of a full viral shell with more than one hundred thousand atoms in less than 2 h on a standard desktop computer. We then compare the two coarse-grained potentials. We show that, despite significant differences in their formulations, the Tirion and the Gō like potentials capture very similar dynamics characteristics of the molecule under study. However, we find that the Gō like potential should be preferred as it leads to less local deformations in the structure of the molecule during normal mode dynamics. Finally, we use NormalGo to characterize the structural transitions that occur when FAB fragments bind to the icosahedral outer shell of serotype 3 of the Dengue virus. We have identified residues at the surface of the outer shell that are important for the transition between the FAB-free and FAB-bound conformations, and therefore potentially useful for the design of antibodies to Dengue viruses.

All-atom normal mode dynamics of HIV-1 capsid

Dynamics of biomolecular assemblies offer invaluable insights into their functional mechanisms. For extremely large biomolecular systems, such as HIV-1 capsid that has nearly 5 millions atoms, obtaining its normal mode dynamics using even coarse-grained models can be a challenging task. In this work, we have successfully carried out a normal mode analysis of an entire HIV-1 capsid in full all-atom details. This is made possible through our newly developed BOSE (Block of Selected Elasticity) model that is founded on the principle of resonance discovered in our recent work. The resonance principle makes it possible to most efficiently compute the vibrations of a whole capsid at any given frequency by projecting the motions of component capsomeres into a narrow subspace. We have conducted also assessments of the quality of the BOSE modes by comparing them with benchmark modes obtained directly from the original Hessian matrix. Our all-atom normal mode dynamics study of the HIV-1 capsid reveals the dynamic role of the pentamers in stabilizing the capsid structure and is in agreement with experimental findings that suggest capsid disassembly and uncoating start when the pentamers become destabilized. Our results on the dynamics of hexamer pores suggest that nucleotide transport should take place mostly at hexamers near pentamers, especially at the larger hemispherical end.

Supramolecular assemblies are large biomolecular complexes composed of hundreds or even thousands of protein chains. They function as molecular machines or as large containers that store or facilitate the chemical reactions of other molecules. Whatever they do, their functional mechanisms are tightly linked to their structures and intrinsic dynamics. Recently, due to breakthroughs in experimental techniques, many supramolecular assemblies have been determined, such as the capsid of human immunodeficiency virus (HIV) that is composed of nearly 5 millions of atoms. Computational studies of these systems are challenging due to their extremely large sizes. In this work, we have successfully carried out a dynamics study of an entire HIV capsid in full all-atom details. Our study reveals new insights into the dynamics of the N-terminal loops, the stabilizing role of the pentamers, and where the nucleotide transport may take place.

Fast Normal Mode Computations of Capsid Dynamics Inspired by Resonance

Increasingly more and larger structural complexes are being determined experimentally. The sizes of these systems pose a formidable computational challenge to the study of their vibrational dynamics by normal mode analysis. To overcome this challenge, this work presents a novel resonance-inspired approach. Tests on large shell structures of protein capsids demonstrate there is a strong resonance between the vibrations of a whole capsid and those of individual capsomeres. We then show how this resonance can be taken advantage of to significantly speed up normal mode computations.

Multiscale virtual particle based elastic network model (MVP-ENM) for normal mode analysis of large-sized biomolecules

In this paper, a multiscale virtual particle based elastic network model (MVP-ENM) is proposed for the normal mode analysis of large-sized biomolecules. The multiscale virtual particle (MVP) model is proposed for the discretization of biomolecular density data. With this model, large-sized biomolecular structures can be coarse-grained into virtual particles such that a balance between model accuracy and computational cost can be achieved. An elastic network is constructed by assuming "connections" between virtual particles. The connection is described by a special harmonic potential function, which considers the influence from both the mass distributions and distance relations of the virtual particles. Two independent models, i.e., the multiscale virtual particle based Gaussian network model (MVP-GNM) and the multiscale virtual particle based anisotropic network model (MVP-ANM), are proposed. It has been found that in the Debye-Waller factor (B-factor) prediction, the results from our MVP-GNM with a high resolution are as good as the ones from GNM. Even with low resolutions, our MVP-GNM can still capture the global behavior of the B-factor very well with mismatches predominantly from the regions with large B-factor values. Further, it has been demonstrated that the low-frequency eigenmodes from our MVP-ANM are highly consistent with the ones from ANM even with very low resolutions and a coarse grid. Finally, the great advantage of MVP-ANM model for large-sized biomolecules has been demonstrated by using two poliovirus virus structures. The paper ends with a conclusion.

Normal mode analysis of Zika virus

In recent years, Zika virus (ZIKV) caused a new pandemic due to its rapid spread and close relationship with microcephaly. As a result, ZIKV has become an obvious global health concern. Information about the fundamental viral features or the biological process of infection remains limited, despite considerable efforts. Meanwhile, the icosahedral shell structure of the mature ZIKV was recently revealed by cryo-electron microscopy. This structural information enabled us to simulate ZIKV. In this study, we analyzed the dynamic properties of ZIKV through simulation from the mechanical viewpoint. We performed normal mode analysis (NMA) for a dimeric structure of ZIKV consisting of the envelope proteins and the membrane proteins as a unit structure. By analyzing low-frequency normal modes, we captured intrinsic vibrational motions and defined basic vibrational properties of the unit structure. Moreover, we also simulated the entire shell structure of ZIKV at the reduced computational cost, similar to the case of the unit structure, by utilizing its icosahedral symmetry. From the NMA results, we can not only comprehend the putative dynamic fluctuations of ZIKV but also verify previous inference such that highly mobile glycosylation sites would play an important role in ZIKV. Consequently, this theoretical study is expected to give us an insight on the underlying biological functions and infection mechanism of ZIKV.

Physical properties of the HIV-1 capsid from all-atom molecular dynamics simulations

Human immunodeficiency virus type 1 (HIV-1) infection is highly dependent on its capsid. The capsid is a large container, made of ∼1,300 proteins with altogether 4 million atoms. Although the capsid proteins are all identical, they nevertheless arrange themselves into a largely asymmetric structure made of hexamers and pentamers. The large number of degrees of freedom and lack of symmetry pose a challenge to studying the chemical details of the HIV capsid. Simulations of over 64 million atoms for over 1 μs allow us to conduct a comprehensive study of the chemical–physical properties of an empty HIV-1 capsid, including its electrostatics, vibrational and acoustic properties, and the effects of solvent (ions and water) on the capsid. The simulations reveal critical details about the capsid with implications to biological function.

The large and complex HIV-1 capsid modulates several molecular events during HIV-1’s infective cycle. Here the authors use all-atom molecular dynamic simulations to probe the biophysical properties of the genome-free HIV-1 capsid.

Comparative Normal Mode Analysis of the Dynamics of DENV and ZIKV Capsids

Key steps in the life cycle of a virus, such as the fusion event as the virus infects a host cell and its maturation process, relate to an intricate interplay between the structure and the dynamics of its constituent proteins, especially those that define its capsid, much akin to an envelope that protects its genomic material. We present a comprehensive, comparative analysis of such interplay for the capsids of two viruses from the flaviviridae family, Dengue (DENV) and Zika (ZIKV). We use for that purpose our own software suite, DD-NMA, which is based on normal mode analysis. We describe the elements of DD-NMA that are relevant to the analysis of large systems, such as virus capsids. In particular, we introduce our implementation of simplified elastic networks and justify their parametrization. Using DD-NMA, we illustrate the importance of packing interactions within the virus capsids on the dynamics of the E proteins of DENV and ZIKV. We identify differences between the computed atomic fluctuations of the E proteins in DENV and ZIKV and relate those differences to changes observed in their high resolution structures. We conclude with a discussion on additional analyses that are needed to fully characterize the dynamics of the two viruses.

MOPS and coxsackievirus B3 stability

Study of coxsackievirus B3 strain 28 (CVB3/28) stability using MOPS to improve buffering in the experimental medium revealed that MOPS (3-morpholinopropane-1-sulfonic acid) increased CVB3 stability and the effect was concentration dependent. Over the pH range 7.0-7.5, virus stability was affected by both pH and MOPS concentration. Computer-simulated molecular docking showed that MOPS can occupy the hydrophobic pocket in capsid protein VP1 where the sulfonic acid head group can form ionic and hydrogen bonds with Arg95 and Asn211 near the pocket opening. The effects of MOPS and hydrogen ion concentrations on the rate of virus decay were modeled by including corresponding parameters in a recent kinetic model. These results indicate that MOPS can directly associate with CVB3 and stabilize the virus, possibly by altering capsid conformational dynamics.

New generation of elastic network models

The intrinsic flexibility of proteins and nucleic acids can be grasped from remarkably simple mechanical models of particles connected by springs. In recent decades, Elastic Network Models (ENMs) combined with Normal Model Analysis widely confirmed their ability to predict biologically relevant motions of biomolecules and soon became a popular methodology to reveal large-scale dynamics in multiple structural biology scenarios. The simplicity, robustness, low computational cost, and relatively high accuracy are the reasons behind the success of ENMs. This review focuses on recent advances in the development and application of ENMs, paying particular attention to combinations with experimental data. Successful application scenarios include large macromolecular machines, structural refinement, docking, and evolutionary conservation.

Three capsid amino acids notably influence coxsackie B3 virus stability

Coxsackievirus B3 strain 28 (CVB3/28) is less stable at 37 °C than eight other CVB3 strains with which it has been compared, including four in this study. In a variant CVB3/28 population selected for increased stability at 37 °C, the capsid proteins of the stable variant differed from the parental CVB3/28 by two mutations in Vp1 and one mutation in Vp3, each of which resulted in altered protein sequences. Each of the amino acid changes was individually associated with a more stable virus. Competition between CVB3/28 and a more stable derivative of the strain showed that propagation of the less stable virus was favoured in receptor-rich HeLa cells.

A Non-Symmetric Reconstruction Technique for Transcriptionally-Active Viral Assemblies

The molecular mechanisms by which RNA viruses coordinate their transcriptional activities are not fully understood. For rotavirus, an important pediatric gastroenteric pathogen, transcription occurs within a double-layered particle that encloses the viral genome. To date, there remains very little structural information available for actively-transcribing rotavirus double-layered particles, which could provide new insights for antiviral development. To improve our vision of these viral assemblies, we developed a new combinatorial strategy that utilizes currently available high-resolution image processing tools. First, we employed a 3D classification routine that allowed us to sort transcriptionally-active rotavirus assemblies on the basis of their internal density. Next, we implemented an additional 3D refinement procedure using the most active class of DLPs. For comparison, the refined structures were computed in parallel by (1) enforcing icosahedral symmetry, and by (2) using no symmetry operators. Comparing the resulting structures, we were able to visualize the continuum that exists between viral capsid proteins and the viral RNA for the first time.

On the relationship between low-frequency normal modes and the large-scale conformational changes of proteins

Normal mode analysis is a computational technique that allows to study the dynamics of biological macromolecules. It was first applied to small protein cases, more than thirty years ago. The interest in this technique then raised when it was realized that it can provide insights about the large-scale conformational changes a protein can experience, for instance upon ligand binding. As it was also realized that studying highly simplified protein models can provide similar insights, meaning that this kind of analysis can be both quick and simple to handle, several applications were proposed, in the context of various structural biology techniques. This review focuses on these applications, as well as on how the functional relevance of the lowest-frequency modes of proteins was established.

Kinetic models for receptor-catalyzed conversion of coxsackievirus B3 to A-particles

The immunoglobulin superfamily protein receptors for poliovirus, human rhinovirus, and coxsackievirus B (CVB) serve to bind the viruses to target cells and to facilitate the release of the virus genome by catalyzing the transition from the mature infectious virus to the A-particle uncoating intermediate. Receptor binding sites characterized by two equilibrium dissociation constants have been identified. The site with higher affinity is best observed at warmer temperatures and appears to correlate with the reversible conformational state in which the capsid is permeable to small molecules and peptides that are buried in the crystal structures are exposed. Measurements of CVB conversion to inactive particles over time in the presence of varied concentrations of soluble coxsackievirus and adenovirus receptor showed that the observed first-order rate constant varies with receptor concentration. The dose-response data, previously modeled as the sum of first-order reactions, have been used to evaluate models for the receptor-catalyzed conversion of CVB that include the high- and low-affinity binding sites associated with capsid breathing. Allosteric models wherein receptor binding shifts the equilibrium toward the open capsid conformation, in which the high-affinity binding site is available, best fit the data.

IMPORTANCE

This paper compares models that relate the structural, mechanistic, and kinetic details of receptor-virus interactions known from previous work with human enteroviruses. New models are derived using recent results from receptor-catalyzed conversion of coxsackievirus B3 to non-infectious A-particles. Of those considered, the acceptable models include the capsid breathing cycle and two conformation-dependent receptor binding sites. The results indicate that the receptor enhancement of virus conversion to A-particles involves allostery through conformation selection.

PIM: phase integrated method for normal mode analysis of biomolecules in a crystalline environment

In this study, a normal mode analysis, named phase integrated method (PIM), is developed for computing modes of biomolecules in a crystalline environment. PIM can calculate low-frequency modes on one or a few asymmetric units (AUs) and generate exact modes of a whole unit cell according to space group symmetry, while the translational symmetry between unit cells is maintained via the periodic boundary condition. Therefore, the method can dramatically reduce computational cost in mode calculation in the presence of crystal symmetry. PIM also has an option to map modes onto a single AU to form an orthonormalized mode set, which can be directly applied to normal-mode-based thermal parameter refinement in X-ray crystallography. The performance of PIM was tested on all 65 space groups available in protein crystals (one protein for each space group) and on another set of 83 ultra-high-resolution X-ray structures. The results showed that considering space group symmetry in mode calculation is crucial for accurately describing vibrational motion in a crystalline environment. Moreover, the optimal inter-AU packing stiffness was found to be about 60% of that of intra-AU interactions (non-bonded interaction only).

Integrin and defensin modulate the mechanical properties of adenovirus

The propensity for capsid disassembly and uncoating of human adenovirus is modulated by interactions with host cell molecules like integrins and alpha defensins. Here, we use atomic force microscopy (AFM) nanoindentation to elucidate, at the single-particle level, the mechanism by which binding of these host molecules affects virus particle elasticity. Our results demonstrate the direct link between integrin or defensin binding and the mechanical properties of the virus. We show that the structure and geometry of adenovirus result in an anisotropic elastic response that relates to icosahedral symmetry. This elastic response changes upon binding host molecules. Whereas integrin binding softens the vertex regions, binding of a human alpha defensin has exactly the opposite effect. Our results reveal that the ability of these host molecules to influence adenovirus disassembly correlates with a direct effect on the elastic strength of the penton region. Host factors that influence adenovirus infectivity thus modulate the elastic properties of the capsid. Our findings reveal a direct link between virus-host interactions and capsid mechanics.

Multiscale macromolecular simulation: role of evolving ensembles

Multiscale analysis provides an algorithm for the efficient simulation of macromolecular assemblies. This algorithm involves the coevolution of a quasiequilibrium probability density of atomic configurations and the Langevin dynamics of spatial coarse-grained variables denoted order parameters (OPs) characterizing nanoscale system features. In practice, implementation of the probability density involves the generation of constant OP ensembles of atomic configurations. Such ensembles are used to construct thermal forces and diffusion factors that mediate the stochastic OP dynamics. Generation of all-atom ensembles at every Langevin time step is computationally expensive. Here, multiscale computation for macromolecular systems is made more efficient by a method that self-consistently folds in ensembles of all-atom configurations constructed in an earlier step, history, of the Langevin evolution. This procedure accounts for the temporal evolution of these ensembles, accurately providing thermal forces and diffusions. It is shown that efficiency and accuracy of the OP-based simulations is increased via the integration of this historical information. Accuracy improves with the square root of the number of historical timesteps included in the calculation. As a result, CPU usage can be decreased by a factor of 3-8 without loss of accuracy. The algorithm is implemented into our existing force-field based multiscale simulation platform and demonstrated via the structural dynamics of viral capsomers.

Virtual interface substructure synthesis method for normal mode analysis of super-large molecular complexes at atomic resolution

Normal mode analysis of large biomolecular complexes at atomic resolution remains challenging in computational structure biology due to the requirement of large amount of memory space and central processing unit time. In this paper, we present a method called virtual interface substructure synthesis method or VISSM to calculate approximate normal modes of large biomolecular complexes at atomic resolution. VISSM introduces the subunit interfaces as independent substructures that join contacting molecules so as to keep the integrity of the system. Compared with other approximate methods, VISSM delivers atomic modes with no need of a coarse-graining-then-projection procedure. The method was examined for 54 protein-complexes with the conventional all-atom normal mode analysis using CHARMM simulation program and the overlap of the first 100 low-frequency modes is greater than 0.7 for 49 complexes, indicating its accuracy and reliability. We then applied VISSM to the satellite panicum mosaic virus (SPMV, 78,300 atoms) and to F-actin filament structures of up to 39-mer, 228,813 atoms and found that VISSM calculations capture functionally important conformational changes accessible to these structures at atomic resolution. Our results support the idea that the dynamics of a large biomolecular complex might be understood based on the motions of its component subunits and the way in which subunits bind one another.

Multiscale simulation of microbe structure and dynamics

A multiscale mathematical and computational approach is developed that captures the hierarchical organization of a microbe. It is found that a natural perspective for understanding a microbe is in terms of a hierarchy of variables at various levels of resolution. This hierarchy starts with the N -atom description and terminates with order parameters characterizing a whole microbe. This conceptual framework is used to guide the analysis of the Liouville equation for the probability density of the positions and momenta of the N atoms constituting the microbe and its environment. Using multiscale mathematical techniques, we derive equations for the co-evolution of the order parameters and the probability density of the N-atom state. This approach yields a rigorous way to transfer information between variables on different space-time scales. It elucidates the interplay between equilibrium and far-from-equilibrium processes underlying microbial behavior. It also provides framework for using coarse-grained nanocharacterization data to guide microbial simulation. It enables a methodical search for free-energy minimizing structures, many of which are typically supported by the set of macromolecules and membranes constituting a given microbe. This suite of capabilities provides a natural framework for arriving at a fundamental understanding of microbial behavior, the analysis of nanocharacterization data, and the computer-aided design of nanostructures for biotechnical and medical purposes. Selected features of the methodology are demonstrated using our multiscale bionanosystem simulator DeductiveMultiscaleSimulator. Systems used to demonstrate the approach are structural transitions in the cowpea chlorotic mosaic virus, RNA of satellite tobacco mosaic virus, virus-like particles related to human papillomavirus, and iron-binding protein lactoferrin.

Photothermal imaging and measurement of protein shell stoichiometry of single HIV-1 Gag virus-like nanoparticles

Virus life stages often constitute a complex chain of events, difficult to track in vivo and in real-time. Challenges are associated with spatial and time limitations of current probes: most viruses are smaller than the diffraction limit of optical microscopes while the entire time scale of virus dynamics spans over 8 orders of magnitude. Thus, virus processes such as entry, disassembly, and egress have generally remained poorly understood. Here we discuss photothermal heterodyne imaging (PHI) as a possible alternative to fluorescence microscopy in the study of single virus-like nanoparticle (VNP) dynamics, with relevance in particular to virus uncoating. Being based on optical absorption rather than emission, PHI could potentially surpass some of the current limitations associated with fluorescent labels. As proof-of-principle, single VNPs self-assembled from 60 nm DNA-functionalized gold nanoparticles (DNA-Au NPs) encapsulated in a Gag protein shell of the human immunodeficiency virus (HIV-1) were imaged, and their photothermal response was compared with DNA-Au NPs. For the first time, the protein stoichiometry of a single virus-like particle was estimated by a method other than electron microscopy.

iMod: multipurpose normal mode analysis in internal coordinates

MOTIVATION

Dynamic simulations of systems with biologically relevant sizes and time scales are critical for understanding macromolecular functioning. Coarse-grained representations combined with normal mode analysis (NMA) have been established as an alternative to atomistic simulations. The versatility and efficiency of current approaches normally based on Cartesian coordinates can be greatly enhanced with internal coordinates (IC).

RESULTS

Here, we present a new versatile tool chest to explore conformational flexibility of both protein and nucleic acid structures using NMA in IC. Consideration of dihedral angles as variables reduces the computational cost and non-physical distortions of classical Cartesian NMA methods. Our proposed framework operates at different coarse-grained levels and offers an efficient framework to conduct NMA-based conformational studies, including standard vibrational analysis, Monte-Carlo simulations or pathway exploration. Examples of these approaches are shown to demonstrate its applicability, robustness and efficiency.

CONTACT

pablo@chaconlab.org

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

All-atom multiscale simulation of cowpea chlorotic mottle virus capsid swelling

An all-atom multiscale computational modeling approach, molecular dynamics/order parameter extrapolation (MD/OPX), has recently been developed for simulating large bionanosystems. It accelerates MD simulations and addresses rapid atomistic fluctuations and slowly varying nanoscale dynamics of bionanosystems simultaneously. With modules added to account for water molecules and ions, MD/OPX is applied to simulate the swelling of cowpea chlorotic mottle virus (CCMV) capsid solvated in a host medium in this study. Simulation results show that the N-terminal arms of capsid proteins undergo large deviations from the initial configurations with their length extended quickly during the early stage of capsid swelling. The capsid swelling is a symmetry-breaking process involving local initiation and front propagation. The capsid swelling rate is approximately 0.25 nm/ns (npn) during the early stage of the simulation, and propagation of the structural transition across the capsid is roughly 0.6 npn. The system conditions that affect swelling of the capsid are analyzed. Prospects for creating a phase diagram for CCMV capsid swelling and using predictions to guide experiments are discussed.

All-atom normal-mode analysis reveals an RNA-induced allostery in a bacteriophage coat protein

Assembly of the T=3 bacteriophage MS2 is initiated by the binding of a 19 nucleotide RNA stem loop from within the phage genome to a symmetric coat protein dimer. This binding event effects a folding of the FG loop in one of the protein subunits of the dimer and results in the formation of an asymmetric dimer. Since both the symmetric and asymmetric forms of the dimer are needed for the assembly of the protein container, this allosteric switch plays an important role in the life cycle of the phage. We provide here details of an all-atom normal-mode analysis of this allosteric effect. The results suggest that asymmetric contacts between the A -duplex RNA phosphodiester backbone of the stem loop with the EF loop in one coat protein subunit results in an increased dynamic behavior of its FG loop. The four lowest-frequency modes, which encompass motions predominantly on the FG loops, account for over 90% of the increased dynamic behavior due to a localization of the vibrational pattern on a single FG loop. Finally, we show that an analysis of the allosteric effect using an elastic network model fails to predict this localization effect, highlighting the importance of using an all-atom full force field method for this problem.

Atomistic modeling of the low-frequency mechanical modes and Raman spectra of icosahedral virus capsids

We describe a technique for calculating the low-frequency mechanical modes and frequencies of a large symmetric biological molecule where the eigenvectors of the Hessian matrix are determined with full atomic detail. The method, which follows order N methods used in electronic structure theory, determines the subset of lowest-frequency modes while using group theory to reduce the complexity of the problem. We apply the method to three icosahedral viruses of various T numbers and sizes; the human viruses polio and hepatitis B, and the cowpea chlorotic mottle virus, a plant virus. From the normal-mode eigenvectors, we use a bond polarizability model to predict a low-frequency Raman scattering profile for the viruses. The full atomic detail in the displacement patterns combined with an empirical potential-energy model allows a comparison of the fully atomic normal modes with elastic network models and normal-mode analysis with only dihedral degrees of freedom. We find that coarse-graining normal-mode analysis (particularly the elastic network model) can predict the displacement patterns for the first few (approximately 10) low-frequency modes that are global and cooperative.

The SAAP force field: development of the single amino acid potentials for 20 proteinogenic amino acids and Monte Carlo molecular simulation for short peptides

Molecular simulation by using force field parameters has been widely applied in the fields of peptide and protein research for various purposes. We recently proposed a new all-atom protein force field, called the SAAP force field, which utilizes single amino acid potentials (SAAPs) as the fundamental elements. In this article, whole sets of the SAAP force field parameters in vacuo, in ether, and in water have been developed by ab initio calculation for all 20 proteinogenic amino acids and applied to Monte Carlo molecular simulation for two short peptides. The side-chain separation approximation method was employed to obtain the SAAP parameters for the amino acids with a long side chain. Monte Carlo simulation for Met-enkephalin (CHO-Tyr-Gly-Gly-Phe-Met-NH2) by using the SAAP force field revealed that the conformation in vacuo is mainly controlled by strong electrostatic interactions between the amino acid residues, while the SAAPs and the interamino acid Lennard-Jones potentials are predominant in water. In ether, the conformation would be determined by the combination of the three components. On the other hand, the SAAP simulation for chignolin (H-Gly-Tyr-Asp-Pro-Glu-Thr-Gly-Thr-Trp-Gly-OH) reasonably reproduced a native-like beta-hairpin structure in water although the C-terminal and side-chain conformations were different from the native ones. It was suggested that the SAAP force field is a useful tool for analyzing conformations of polypeptides in terms of intrinsic conformational propensities of the single amino acid units.

Vibrational dynamics of icosahedrally symmetric biomolecular assemblies compared with predictions based on continuum elasticity

Coarse-grained elastic network models elucidate the fluctuation dynamics of proteins around their native conformations. Low-frequency collective motions derived by simplified normal mode analysis are usually involved in biological function, and these motions often possess noteworthy symmetries related to the overall shape of the molecule. Here, insights into these motions and their frequencies are sought by considering continuum models with appropriate symmetry and boundary conditions to approximately represent the true atomistic molecular structure. We solve the elastic wave equations analytically for the case of spherical symmetry, yielding a symmetry-based classification of molecular motions together with explicit predictions for their vibrational frequencies. We address the case of icosahedral symmetry as a perturbation to the spherical case. Applications to lumazine synthase, satellite tobacco mosaic virus, and brome mosaic virus show that the spherical elastic model efficiently provides insights on collective motions that are otherwise obtained by detailed elastic network models. A major utility of the continuum models is the possibility of estimating macroscopic material properties such as the Young's modulus or Poisson's ratio for different types of viruses.

The structural dynamics of macromolecular processes

Dynamic processes involving macromolecular complexes are essential to cell function. These processes take place over a wide variety of length scales from nanometers to micrometers, and over time scales from nanoseconds to minutes. As a result, information from a variety of different experimental and computational approaches is required. We review the relevant sources of information and introduce a framework for integrating the data to produce representations of dynamic processes.

Molecular dynamics/order parameter extrapolation for bionanosystem simulations

A multiscale approach, molecular dynamics/order parameter extrapolation (MD/OPX), to the all-atom simulation of large bionanosystems is presented. The approach starts with the introduction of a set of order parameters (OPs) automatically generated with orthogonal polynomials to characterize the nanoscale features of bionanosystems. The OPs are shown to evolve slowly via Newton's equations, and the all-atom multiscale analysis (AMA) developed earlier (Miao and Ortoleva, J Chem Phys 2006, 125, 44901) demonstrates the existence of their stochastic dynamics, which serve as the justification for our MD/OPX approach. In MD/OPX, a short MD run estimates the rate of change of the OPs, which is then used to extrapolate the state of the system over time that is much longer than the 10(-14) second timescale of fast atomic vibrations and collisions. The approach is implemented in NAMD and demonstrated on cowpea chlorotic mottle virus (CCMV) capsid structural transitions (STs). It greatly accelerates the MD code and its underlying all-atom description of the nanosystems enables the use of a universal interatomic force field, avoiding recalibration with each new application as needed for coarse-grained models. The source code of MD/OPX is distributed free of charge at https://simtk.org/home/mdopx and a web portal will be available via http://sysbio.indiana.edu/virusx.

Deformation of biological cells in the acoustic field of an oscillating bubble

In this work we develop a theoretical framework of the interaction of microbubbles with bacteria in the ultrasound field using a shell model of the bacteria, following an approach developed previously [P. V. Zinin, Phys. Rev. E 72, 61907 (2005)]. Within the shell model, the motion of the cell in an ultrasonic field is determined by the motion of three components: the internal viscous fluid, a thin elastic shell, and the surrounding viscous fluid. Several conclusions can be drawn from the modeling of sound interaction with a biological cell: (a) the characteristics of a cell's oscillations in an ultrasonic field are determined both by the elastic properties of the shell the viscosities of all components of the system, (b) for dipole quadrupole oscillations the cell's shell deforms due to a change in the shell area this oscillation depends on the surface area modulus K{A} , (c) the relative change in the area has a maximum at frequency f{K} approximately 1/2pi square root[K{A}(rhoa;{3})] , where a is the cell's radius and rho is its density. It was predicted that deformation of the cell wall at the frequency f{K} is high enough to rupture small bacteria such as E . coli in which the quality factor of natural vibrations is less than 1 (Q<1). For bacteria with high value quality factors (Q>1) , the area deformation has a strong peak near a resonance frequency f{K} however, the value of the deformation near the resonance frequency is not high enough to produce sufficient mechanical effect. The theoretical framework developed in this work can be extended for describing the deformation of a biological cell under any arbitrary, external periodic force including radiation forces unduced by acoustical (acoustical levitation) or optical waves (optical tweezers).

Group theory of icosahedral virus capsid vibrations: a top-down approach

We explore the use of a top-down approach to analyse the dynamics of icosahedral virus capsids and complement the information obtained from bottom-up studies of viral vibrations available in the literature. A normal mode analysis based on protein association energies is used to study the frequency spectrum, in which we reveal a universal plateau of low-frequency modes shared by a large class of Caspar-Klug capsids. These modes break icosahedral symmetry and are potentially relevant to the genome release mechanism. We comment on the role of viral tiling theory in such dynamical considerations.

Twenty-four near-instabilities of Caspar-Klug viruses

Group theoretical arguments combined with normal mode analysis techniques are applied to a coarse-grained approximation of icosahedral viral capsids which incorporates areas of variable flexibility. This highlights a remarkable structure of the low-frequency spectrum in this approximation, namely, the existence of a plateau of 24 near zero modes with universal group theory content.